The musing followed interim Liberal leader Bob Rae's comment that Mulroney's government changed the Members of Parliament Retiring Allowances Act just as he was leaving office so that prime ministers would get the equivalent of two-thirds of his or her salary at age 65.

In fact, the retirement allowance for prime ministers was actually brought in under the Liberal government of Lester Pearson and later revised under Pierre Trudeau. The Grits have since apologized for the mistake.

Mulroney posted a link to an iPolitics.ca story that clarified that the retirement allowance was Pearson's policy, not his father's.

"For your reading pleasure, @nspector4," Mulroney tweeted.

Spector replied he may have been the first person to post a link to the iPolitics.ca story.

"@nspector4 I just saw that you tweeted it," Mulroney replied. "Too bad it didn't include a retraction of your insinuation of a "secret deal". #researchisdead."

Spector wrote that he was only raising a quiet deal as a possible explanation for the "peculiar absence" of media coverage of the retirement allowance in 1992 and that he "tweeted real explanation 2 hours ago."

"@nspector4 Well, wild unsubstantiated accusations is certainly one way to go," Mulroney responded. "How that jives with your 'facts are facts' mantra is beyond me."

Mulroney, a television personality, fired off one last tweet: "@nspector4 .... but what do I know, I'm just a game show host."

"No accusation just a question," Spector wrote back. "As soon as facts established by iPolitics (which broke story few days ago) tweeted it @BenMulroney1976."

This is the second time in less than a month that Mulroney has publicly stood up for his dad.

The Toronto Star published a letter last month in which he disputed a columnist's claim that his father stepped down in 1993 rather than face an election because his poll numbers were low. Mulroney pointed to a Globe and Mail story showing the Tories and Liberals were in a dead heat in August 1993.

"If (columnist Bob) Hepburn's claim is to be swallowed, the numbers stated above must be ignored," Mulroney wrote.

"But when it comes to the Star, denigrating a particular Progressive Conservative prime minister often trumps the truth."

Maclean's magazine political editor Paul Wells spotted the letter and tweeted that Mulroney was using a poll from the early days of Tory prime minister Kim Campbell's leadership to prove his father was well-loved.

"Not once did I suggest be was popular when he resigned Paul. It would be foolish to do so," Mulroney tweeted back.

"I suggested that Bob's contention that the people were so fed up that they booted the PCs from office doesn't hold water. Undo unsurprising given source."